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The only legal way is to receive them from an official pokemon event, and since those games almost a decade old and 3 generations ago, its highly unlikely they will have one.

Honestly, if you want one, just hack it, if you are really nuts you could try to go find someone with a legal mew that they clones legally in emerald with the cloning glitch... but since gen 3 isn't connectable to the internet you would have to meet them personally to trade...

You could get a legit mew in yellow without gameshark, though the method to do so is so out of the ordinary I often wonder how people even figured it out...

Its not that amazing honestly, eventually someone was going to attempt to fly or teleport from a battle by opening up the menu.

The reason why you have to find a slowbro is because of the slowbro's special stat. It turns out that when you enter a battle in gen 1 the way the game determines what pokemon you will fight is left in the same value used for the special stat. For a usual battle this is preordained by what special stat or enemy pokemon values a trainer has. On game freaks part this is just lazy and kinda stupid programming, like how they store your name as a wild pokemon for the old man fight. So by flying out of the battle, you keep the special stat of the opposing pokemon and the game has left in its program that you need to battle the guy on that route. So when you return to that route, the game uses the special stat of the pokemon you last fought and flew from to decide what you fight. Mew has a enemy pokemon indicated that is the same as slowbro's special, so it works.